Year 8 Scheme of Work S Course

Topic / Links to NC / PLTs / Learning Objectives / Learning Outcomes/Success Criteria/Assessment / Resources / Cross curricular links/Key words/Points to note
1. Decimal calculation (4 lessons) / 36 – 39 Understand and use decimal notation and place value, multiply and divide integers and decimals by 10, 100, 1000, and explain the effect.
AB Use 1 d.p. and 2 d.p.
C Multiply and divide decimals by 10, 100…
92 – 101 Consolidate and extend mental methods of calculation to include decimals, fractions and percentages, accompanied where appropriate by suitable jottings: solve simple word problems mentally.
A Add, subtract, multiply, divide 1 d.p.
D Calculate with metric measures.
104 – 105 Use standard column procedures to add, subtract whole numbers and decimals with up to two decimal places.
AB Add, subtract 1,2 d.p.
B Add subtract to 2 d.p.
104 – 107 Multiply and divide three-digit by two-digit whole numbers, extend to multiplying and dividing decimals with one or two places by single-digit whole numbers.
AB Multiply, divide 1,2 d.p.
108 – 109 Enter numbers and interpret the display in different contexts (decimals, percentages, money, metric measures)
18EFG Multiply, divide in money contexts.
228 – 231 Use names and abbreviations of units of measurement to measure, estimate, calculate and solve problems in everyday contexts, involving length, area, mass, capacity, time and angle; convert one metric unit to another (e.g. grams to kilograms); read and interpret scales on a range of measuring instruments.
18D Convert between metric units. / TW
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EP / Use the four arithmetic operations to solve simple questions and problems using decimals to one or two decimal places.
Read scales to one decimal place.
Multiply and divide decimals by powers of ten.
Convert metric units of length, mass and capacity
Estimate costs of everyday items
Use a unitary method to compare prices.
MPA ~ use appropriate mathematical procedures
Build on the approach to calculation which emphasises mental and written methods that are gradually refined.
Visualising imagines such as number lines to support mental methods. / ALL WILL:
Calculate with decimals without using a calculator.
MOST WILL:
Use a calculator to calculate with decimals.
Assessment criteria:
(N) Level 4 ~ order decimals to three decimal places
(C) Level 4 ~ multiply a simple decimal by a single digit
(N) Level 5 ~ round decimals to the nearest decimal place
(S) Level 5 ~ solve problems involving the conversion of units / S1 chapter 18
7S chapter 24
10 Ticks:
Level 4 Pack 3 15-20
Level 4 Pack 4 33-38
Level 5 Pack 2 21-24 / Decimal places,
2. Fair to all (3 lessons) / 2 – 25 Solve word problems and
investigate in a range of contexts:
number, algebra, shape, space and
measure, and handling data, compare and
evaluate solutions.
26 – 27 Identify the necessary to solve a problem; represent problems mathematically, making correct use of symbols, words, diagrams, tables and graphs.
28 – 29 Break a complex calculation into simpler steps, choosing and using appropriate and efficient operations, methods and resources, including ICT.
30 – 31 Present and interpret solutions in the context of the original problem; and justify methods and conclusions, orally and in writing.
32 – 35 Suggest extensions to problems by asking “what if …?, begin generalise and to understand the significance of a counter-example.
B Word count investigation.
256 – 261 Calculate statistics for small sets of discrete data; find the mode, median and range, and the modal class for grouped data; calculate the mean, including from a simple frequency table, using a calculator for a larger number of items.
AB Mean, including from frequency table.
C Median, mead, mode
248 - 249 Discuss a problem that can be addressed by stastical methods and identify related questions to explore.
B Word count investigation.
250 – 251 Decide which data to collect to answer a question, and the degree of accuracy needed; identify possible sources.
B Word count investigation.
252 – 254 Plan how to collect the data, including sample size; construct frequency tables with given equal class intervals for sets of continuous data, design and use two-way tables for discrete data.
B Word count investigation.
254 – 255 Collect data using a suitable method such as observation, controlled experiment, including data logging using ICT, or questionnaire.
B Word count investigation.
272 – 273 Communicate orally and on paper the results of a statistical enquiry and the methods used, using ICT as appropriate; justify the choice of what is presented.
B Word count investigation. / TW
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EP / Calculate the mean of a list of numbers.
Calculate the mean from a frequency table.
Calculate the mean, median and mode and decide which value is the most representative average.
MPA ~ use appropriate mathematical procedures
Calculate summary statistics, for example, measures of average and spread
MPA Interpreting and evaluating
Considering the effects of changes to the data / ALL WILL:
Calculate the mean of a set of data
MOST WILL:
Calculate the mean from a frequency table
SOME WILL:
Know what is meant by mean, mode and median and which “is better” in a given situation
Assessment criteria:
(H) Level 4 ~ understand the mode and range to describe sets of data
(H) Level 5 ~ understand and use the mean of discrete data and compare two simple distributions, using the range and one of mode, median and mean
(U) Level 5 ~ check results, considering whether they are reasonable
(U) Level 5 ~ draw simple conclusions of their own and give an explanation of their reasoning / S1 chapter 21
7S chapter 46
10 Ticks:
Level 5 Pack 6 3-6
NRICH Task
Searching for Mean(ing) / Mean, mode, median,
3. Percentage (4 lessons) / 70 – 77 Understand percentage as the “number of parts per 100”; recognise the equivalence of percentages, fractions and decimals: calculate simple percentages and use percentages to compare simple proportions.
A Parts per 100 on a scale.
CDE Relate percentage, fractions and decimals.
D Calculate a percentage of a quantity.
F Express one number as a percentage of another.
G Display and compare proportions.
92 – 101 Consolidate and extend mental methods of calculation to include decimals, fractions and percentages, accompanied where appropriate by suitable jottings: solve simple word problems mentally.
B Calculate percentage.
268 – 271 Interpret diagrams and graphs (including pie charts), and draw simple conclusions based on the shape of graphs and simple statistics for a single distribution.
20D Pie charts. / TW
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EP / Change a percentage to a decimal
Calculate a percentage of a quantity
Calculate one quantity as a percentage of another
Construct pie charts from percentages.
MPA ~ use appropriate mathematical procedures
Extend procedures to calculations with fraction, decimals and percentages
MPA Communicating and reflecting
Use precise language and symbolism to set out solutions in an organized and understandable way / ALL WILL:
Change percentages into decimals
MOST WILL:
Calculate percentages of quantities both in my head and using a calculator
SOME WILL:
Calculate one quantity as a percentage of another
Assessment criteria:
(N) Level 4 ~ recognise approximate proportions of a whole and use simple fractions and percentages to describe these
(N) Level 6 ~ use the equivalence of fractions, decimals and percentages to compare proportions
(C) Level 6 ~ calculate percentages
(U) Level 5 ~ check results, considering whether they are reasonable
(U) Level 5 ~ show an understanding of situations by describing them mathematically using symbols, words and diagrams / S1 chapter 20
7S chapter 45
10 Ticks:
Level 4 Pack 4 21-28
Level 5 Pack 2
28-32 35-36
Level 6 Pack 3 3-16
ePack:
ePack C 6-7
ePack D 3-8
ePack E 9
NRICH Task
Percentage of Percentages / Percentage, Equivalent, Fraction, Decimal, Cancelling, Pie Chart,
4. Negative numbers (3 lessons) / 48 – 51 Understand negative numbers as positions on a number line, order, add and subtract positive and negative integers in context.
22AB Number line, order positive and negative numbers in context.
22CDAdd, subtract positive and negative integers. / TW
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EP / Compare positive and negative numbers.
Add and subtract negative numbers.
MPA Communicating and reflecting
Linking mental methods with jottings and representations, for example, on a number line / ALL WILL:
Compare positive and negative numbers.
MOST WILL:
Add negative numbers.
Subtract negative numbers
Assessment criteria:
(N) Level 3 ~ recognise negative numbers in contexts such as temperature
(C) Level 5 ~ solve simple problems involving ordering, adding and subtracting negative numbers in context
(N) Level 5 ~ order negative numbers / S1 chapter 22
7S chapter 48
10 Ticks:
Level 4 Pack 3 11-13
Level 5 Pack 4 3-21
NRICH Tasks
Consecutive Negative Numbers
Adding and Subtracting Positive and Negative Numbers / Negative numbers, number line.
5. Transformations (4 lessons) / 202 – 203 Understand and use the language and notation associated with reflections, translations and rotations.
A Reflect
B Rotate
C Translate.
202 – 212 Recognise and visualise the transformation and symmetry of a 2-d shape, reflection in a given mirror line, and line symmetry: rotation about a given point and rotation symmetry: translation, explore these transformations and symmetries using ICT.
A Reflection.
B Rotation.
C Translation. / TW
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EP / Follow instructions for transformations (reflections, rotations and translations)
Describe transformations clearly.
MPA Analysisng ~ use mathematical reasoning
Visualise and work with images, explaining relationships within an image; for example, transforming an image and identifying changes and what stays the same / ALL WILL:
Reflect, rotate and translate shapes
SOME WILL:
Describe transformations.
Assessment criteria:
(S) Level 4 ~ reflect simple shapes in a mirror line, translate shapes horizontally or vertically and begin to rotate shapes about its centre or vertex
(S) Level 5 ~ reason about position and movement and transform shapes
(S) Level 6 ~ know that translation, rotations and reflections preserve length and angle and maps objects onto congruent images / S1 chapter 23
7S chapter 47
10 Ticks:
Level 4 Pack 7 29-38
Level 5 Pack 4 31-35
Level 6 Pack 2 3-22
Level 7 Pack 4 31-33
Also need: mirrors, tracing paper
NRICH Tasks
Simplifying Transformations / Mirror line, perpendicular, Centre of rotation, clockwise, anti-clockwise, turn, vertices, coordinates, column vector, axis, origin.
Assessment 1 / Assessment is based on decimals, fair to all, percentages, negative numbers and transformations. / TW
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6. Functions and graphs (4 lessons) / 112 –113 Begin to distinguish the different roles played by letter symbols in equations, formulae and functions; know the meaning of the words formula and function.
A Use of function.
164 – 167 Generate coordinate pairs that satisfy a simple linear rule; plot the graphs of simple linear functions, where y is given explicitly in terms of x, on paper and using ICT, recognising straight-line graphs parallel to the x-axis or y-axis.
B Generate pairs and plot.
C Recognise function represented by graph parallel to axis.
172 – 177 Begin to plot and interpret the graphs of simple linear functions arising from real-life situations.
A Plot linear graph from situation.
160 – 163 Express simple functions in symbols, represent mappings expressed algebraically.
C Generate pairs of values for function.
164 – 167 Generate points in all four quadrants and plot the graphs of linear functions, where y is given explicitly in terms of x, on paper and using ICT, recognise that equations of the form y=mx+c correspond to straight-line graphs.
D Generate pairs and plot in all four quadrants. / TW
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EP / Draw a graph based on a rule.
Find the equation of a straight-line graph.
MPA Representing
Developing understanding of algebraic conventions…coordinate points and equations of lines / ALL WILL:
Write a table of values and draw a graph for a situation described in words.
Find information from a graph.
MOST WILL:
Draw the graph of a function like y=x+3.
SOME WILL:
Find the equation of a straight line graph
Assessment criteria:
(A) Level 5 ~ use and interpret coordinates in all four quadrants
(A) Level 6 ~ plot the graphs of linear functions
(A) Level 6 ~ recognise that equations of the form y = mx + c correspond to straight line graphs / S1 chapter 24
7S chapter 51
10 Ticks:
Level 6 Pack 1 25-28
Level 7-8 Pack 1 21
NRICH Tasks
Diamond Collector / Gradient, intercept, graph, coordinates, quadrants,
7. Multiples and factors (3 lessons) / 52 – 55 Recognise and use multiples, factors (divisors), common factor, HCF and LCM in simple cases, and primes (less than 100); use simple tests of divisibility
25ABCMultiple, factor, prime.
25D Tests of divisibility.
25EGHCommon multiple, lowest common multiple.
25FGCommon factor, highest common factor. / TW
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EP / Understand; multiples, factors, common multiples and common factors.
Recognise prime numbers.
MPA Representing
Identifying the type of problem and the operations needed to reach a solution / ALL WILL:
Explain what multiple means.
Explain what factor means.
Explain what a prime number is.
MOST WILL:
Explain what lowest common multiple is.
Explain what highest common factor means.
SOME WILL:
Use some tests of divisibility.
Assessment criteria:
(A) Level 3 ~ recognise a wider range of sequences
(N) Level 4 ~ recognise and describe number relationships including multiple, factor and square
(N) Level 5 ~ recognise and use number patterns and relationships / S1 chapter 25
7S chapter 52
10 Ticks:
Level 5 Pack 1 26-27
Also need: Sheet 175, 134,176,177
NRICH Task
Factors and Multiples Resources / Prime, multiple, lowest common multiple, factor, highest common factor,
8. Know your calculator (3 lessons) / 56 – 59 Recognise the first few triangular numbers, squares of numbers to at least 12x12 and the corresponding roots.
FG Square, square root.
86 – 87 Know and use the order of operations, including brackets.
ABCDIOrder of operations, brackets.
86 – 87 Use the order of operations, including brackets, with more complex calculations.
I Order of operations, complex expression.
108 – 109 Carry out calculations with more than one step using brackets and the memory, use the square root and sign change keys.
A Priority of operations.
BDI Brackets.
CD Bracketing effect of horizontal line for division.
E Memory
G Square root.
H Sign change key.
108– 109 Carry out more difficult calculations effectively and efficiently using the function keys for sign change, powers, roots and fractions; use brackets and the memory.
DEFGHIUse of sign changes, powers, root, brackets and memory. / TW
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EP / Use a calculator effectively, including the bracket, square, square root, memory and sign-change keys.
Learn rules to find the value of expressions with more than one operation.
MPA Representing
Breaking more complex problems into a sequence of steps
MPA Analysisng ~ use mathematical reasoning
Use different techniques to analyse a situation, evalute an approach or check a calculation
MPA ~ use appropriate mathematical procedures
Developing efficient use of calculators and spreadsheets / ALL WILL:
Work out the value of an expression that involves more than one operation and may include brackets.
MOST WILL:
Calculate to find the value of an expression
Assessment criteria:
(N) Level 4 ~ recognise square numbers
(C) Level 7 ~ use a calculator efficiently and appropriately to perform complex calculations with numbers of any size / S1 chapter 26
7S chapter 53
10 Ticks:
Level 5 Pack 5 3-7
Also need Sheet 179 / BODMAS, brackets, memory, powers, calculator, square root
9. Investigations (2 lessons) / 2 – 25 Solve word problems and investigate in a
range of contexts: number, algebra, shape, space
and measure, and handling data, compare and
evaluate solutions.
26 – 27 Identify the necessary to solve a problem; represent problems mathematically, making correct use of symbols, words, diagrams, tables and graphs.
28 – 29 Break a complex calculation into simpler steps, choosing and using appropriate and efficient operations, methods and resources, including ICT.
30 – 31 Present and interpret solutions in the context of the original problem; and justify methods and conclusions, orally and in writing.
32 – 35 Suggest extensions to problems by asking “what if …?, begin generalise and to understand the significance of a counter-example.
Investigations and how to report them.
56 – 59 Recognise the first few triangular numbers, squares of numbers to at least 12x12 and the corresponding roots.
A Triangle number.
154 – 157 Generate sequences from practical contexts and describe the general term in simple cases.
AB Generate sequence from investigation, describe a general term.
224 – 227 Find simple loci, both by reasoning and by using ICT, to produce shapes and paths, e.g. an equilateral triangle.
B Path from rules. / TW
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EP / Solve a mathematical investigation.
Write up a mathematical investigation in a logical and sequential way.
MPA Communicating and reflecting
Discuss and reflect on different approaches to solving a problem
MPA Analysisng ~ use mathematical reasoning
Making generalizations, explaining and proving, and relating results to the context of the problem / ALL:
Attempt a mathematical investigation.
MOST/SOME:
Write up a mathematical investigation in such a way that the reader will understand the problem, the approaches I used, the results I obtained and their meaning as well as any modifications I have made to the original problem.
Assessment criteria:
(U) Level 4 ~ develop own strategies for solving problems
(U) Level 4 ~ Use their own strategies within Mathematics and in applying Mathematics to practical contexts
(U) Level 4 ~ present information and results in a clear and organised way
(U) Level 5 ~ check results
(U) Level 5 ~ draw simple conclusions of their own and give an explanation of their reasoning
(U) Level 6 ~ solve problems and carry through substantial tasks by breaking them into smaller, more manageable tasks
(U) Level 6 ~ present a concise, reasoned argument, using symbols, graphs and related explanatory tasks / S1 chapter 12
7S chapter 42
10Ticks:
Level 5 Pack 1 28, 38
Level 6 Pack 1 31-32
10. Into the bath (1 lesson) / 172 – 177 Construct linear functions arising from real-life problems and plot their corresponding graphs; discuss and interpret graphs arising from real situations.
Interpret graphs from real life. / TW
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EP / Obtain information from graphs.
Sketch graphs describing real situations.
MPA Communicating and reflecting
Communicate own findings effectively / ALL:
Obtain information from graphs.
Sketch graphs describing real situations.
Assessment criteria:
(S) Level 2 ~ use everyday units to measure length and weight
(S) Level 3 ~ understand units of length, capacity, weight and time, and use these
(S) Level 4 ~ read accurately from a ruler and other scales
Level 4 ~ draw line graphs
(H) Level 5 ~ interpret graphs and diagrams and draw conclusions / S2 chapter 1
8S chapter 1
10Ticks:
Level 4 Pack 6 17-19
Level 5 Pack 6 19-22
Level 6 Pack 5 3-4 / Water, graph, depth, axis, scale, origin, coordinates
11. Ratios (4 lessons) / 78 – 81 Consolidate understanding of the relationship between ratio and proportion; reduce a ratio to its simplest form, including a ratio expressed in different units, recognising links with fraction notation; divide a quantity into two or more parts in a given ratio; use the unitary method to solve simple word problems involving ratio and direct proportion.